We present an analysis of the positioning errors in Backprojection (BP)-based Synthetic Aperture Radar (SAR) images due to antenna trajectory errors for a monostatic SAR traversing a straight linear trajectory. Our analysis is developed using microlocal analysis, which can provide an explicit quantitative relationship between the trajectory error and the positioning error in BP-based SAR images. The analysis is applicable to arbitrary trajectory errors in the antenna and can be extended to arbitrary imaging geometries. We present numerical simulations to demonstrate our analysis.

We present a novel method for ground moving target detection and imaging using a SAR system transmitting
ultra-narrowband continuous waveforms. We develop a new forward model that relates the velocity as well as
reflectivity information at each location to a correlated received signal. We reconstruct moving target images
by a filtered-backprojection method. We use the image contrast as a metric to detect moving targets and
to determine their velocities. The method results in well-focused reflectivity images of moving targets and
their velocity estimates regardless of the target location, speed, and velocity direction. We present numerical
experiments to verify our method.

We present a novel passive radar imaging method for moving targets using distributed apertures. We develop a
passive measurement model that relates measurements at a given receiver to measurements at other receivers.
We formulate the passive imaging problem as a Generalized likelihood ratio test (GLRT) for a hypothetical
target located at an unknown position, moving with an unknown velocity. We design a linear discriminant
functional by maximizing the signal-to-noise ratio (SNR) of the test-statistic, and use the resulting position- and
velocity-resolved test-statistic to form an image of the scene of interest. We present numerical experiments to
demonstrate the performance of our imaging method.

We consider synthetic aperture radar system using ultra-narrowband continuous waveforms, which we refer to
as Doppler Synthetic Aperture Radar (DSAR). We present a novel image formation method for bi-static DSAR.
Our method first correlates the received signal with a scaled or frequency-shifted version of the transmitted signal
over a finite time window, and then uses microlocal analysis to reconstruct the scene by a filtered-backprojection
of the correlated signals. Our approach can be used under non-ideal imaging scenarios such as arbitrary flight
trajectories and non-flat topography. Furthermore, it is an analytic reconstruction technique which can be made
computationally efficient. We present numerical experiments to demonstrate the performance of the proposed
method.

We present a novel passive image formation method for moving targets using distributed apertures capable
of exploiting information about multiple-scattering in the environment. We assume that the environment is
illuminated by non-cooperative transmitters of opportunity with unknown location and unknown transmitted
waveforms. We develop a passive measurement model that relates the scattered field from moving targets at a
given receiver to the scattered field at other receivers. We formulate the passive imaging problem as a generalized
likelihood ratio test for a hypothetical target located at an unknown position, moving with an unknown velocity.
We design a linear discriminant functional by maximizing the Signal-to-Noise Ratio (SNR) of the test-statistic,
and use the resulting position- and velocity-resolved test-statistic to form the image. Our imaging method can
determine the two- or three-dimensional velocity vector as well as the two- or three-dimensional position vector
of a moving target without the knowledge of transmitter locations and transmitted waveforms. We present
numerical experiments to demonstrate the performance of our passive imaging method operating in multiplescattering
environments. The results show that the point spread function of the reconstructed images improves
when the information about multiple scattering is exploited.

We consider passive airborne receivers that use backscattered signals from sources of opportunity transmitting
fixed-frequency waveforms, which we refer to as Doppler Synthetic Aperture Hitchhiker (DSAH). We present a
novel image formation method for DSAH. Our method first correlates the windowed signal obtained from one
receiver with the windowed, filtered, scaled and translated version of the received signal from another receiver,
and then uses the microlocal analysis to reconstruct the scene radiance by the weighted-backprojection of the
correlated signal. This imaging algorithm can put the visible edges of the scene radiance at the correct location,
and under appropriate conditions, with correct strength. We show that the resolution of the image is directly
related to the length of the support of the windowing function and the frequency of the transmitted waveform.
We present numerical experiments to demonstrate the performance of the proposed method.

The Chirp-Scaling Algorithm (CSA) is one of the most widely used synthetic aperture radar (SAR) image
reconstruction method. However, its applicability is limited to straight flight trajectories and monostatic SAR.
We present a new mathematical treatment of the CSA from the perspective of Fourier Integral Operators theory.
Our treatment leads to a chirp-scaling-based true amplitude imaging algorithm, which places the visible edges of
the scene at the correct locations and directions with the correct strength. Furthermore, it provides a framework
for the extension of the chirp-scaling based approach to non-ideal imaging scenarios as well as other SAR imaging
modalities such as bistatic-SAR and hitchhiker-SAR.

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